Checkpoint 3 of 3 10 MC + 2 Short Answer Covers Lessons 15-20

Checkpoint 3

Probability. Assess your understanding of simple and compound probability, tree diagrams, Venn diagrams, two-way tables, theoretical vs experimental probability and conditional probability.

Instructions: Complete all questions. For multiple choice, select one answer and click Check. For short answer, show all working. Your responses are saved automatically.

Section A - Multiple Choice

2 marks each. Select the best answer.

2 marks A fair die is rolled. The probability of rolling an even number is:

1/6 1/3 1/2 2/3

2 marks If P(A) = 0.4, then P(not A) =

0.4 0.5 0.6 1

2 marks Two independent events have P(A) = 0.3 and P(B) = 0.5. P(A and B) =

0.8 0.15 0.2 0.35

2 marks A card is drawn from a deck, not replaced, then a second card is drawn. The events are:

Independent Dependent Mutually exclusive Certain

2 marks In a Venn diagram, the overlapping region of two circles represents:

Elements in A only Elements in B only Elements in both A and B Elements in neither A nor B

2 marks A coin is tossed 100 times and lands on heads 48 times. The experimental probability of heads is:

0.48 0.50 0.52 48

2 marks P(A or B) for non-mutually exclusive events is:

P(A) + P(B) P(A) + P(B) − P(A and B) P(A) × P(B) 1 − P(A and B)

2 marks If P(A and B) = 0.2 and P(B) = 0.4, then P(A|B) =

0.2 0.5 0.6 0.8

2 marks On a tree diagram, to find the probability of a path you:

Add probabilities along branches Multiply probabilities along branches Subtract probabilities Divide probabilities

2 marks The law of large numbers states that as the number of trials increases:

Experimental probability approaches theoretical probability Theoretical probability becomes zero All probabilities become equal Outcomes become certain

Section B - Short Answer

Show all working. 5 marks each.

Question 11

5 marks Apply / Analyse

A bag contains 5 red, 3 blue and 2 green marbles. Two marbles are drawn without replacement.

(a) Draw a tree diagram showing the first and second draws. Label all probabilities. (2 marks)

(b) Calculate the probability of drawing two red marbles. (1 mark)

Question 12

5 marks Analyse / Evaluate

In a school of 200 students, 80 play basketball, 60 play soccer, and 30 play both sports.

(a) Complete a Venn diagram or two-way table for this information. (2 marks)

(b) Calculate the probability that a randomly chosen student plays basketball or soccer (or both). (1 mark)

I have completed Checkpoint 3 and checked my answers.